On the asymptotic behavior of perturbed strongly continuous semigroups (Q2729616)
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scientific article; zbMATH DE number 1623081
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the asymptotic behavior of perturbed strongly continuous semigroups |
scientific article; zbMATH DE number 1623081 |
Statements
23 May 2002
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strongly continuous semigroup
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perturbation
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spectrum
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growth bound
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norm continuity
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compactness
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Dyson-Phillips series
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On the asymptotic behavior of perturbed strongly continuous semigroups (English)
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The author considers a strongly continuous semigroup with generator \(A\) on a Banach space and an \(A\)-bounded perturbation \(B\). He characterizes the norm continuity and compactness of the terms in the Dyson-Phillips series of a perturbed semigroup. Uniform exponential stability of the perturbed semigroup is characterized by spectral conditions. The results are applied to a delay differential equation.
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